# trigonometry's questions - English 1answer

275 trigonometry questions.

### 1 Indefinite ArcTan integral does not return the (known) real expression but returns complex expression

1 answers, 53 views calculus-and-analysis trigonometry
I have a problem with an indefinite integral which I solved using MMA in back in 2010 (must have been version 7 or 8) successfullly and it gave an elegant result. However, if I run it with MMA 11.3 (...

### 3 Indeterminate result from Sinc

1 answers, 105 views error fourier-analysis trigonometry
I have an impulse train given by(1 + Csc[(π x)/(1 + R)] Sin[(π (1 + 2 R) x)/(1 + R)])/(2 + 2 R)Because of the Csc, ...

### 4 Solve/Reduce not working on a function with a condition/domain restriction?

I'm working with a trigonometric function, so I thought it would be convenient to set a condition to restrict the domain so I wouldn't have to specify it in the solve function each time. Here is a ...

### 12 Factorize trigonometric matrices

Consider two square matrices $A_1$ and $A_2$. Consider the following matrix involving matrix trigonometric functions: M_1(t)=\begin{bmatrix} \cos(tA_1) & t\mathrm{sinc}(t A_1) \\ ...

### 3 Prevent Trigonometric simplifications from using double angle and half angle formulae?

Is there any way to force Mathematica to not use double and half angle formulae etc. when simplifying Trigonometric expressions? For example,...

### 2 Convert trigonometric expression into other forms using just a specific set of identities

I am trying to convert a trigonometric expression likesinθ/(1 - cosθ)intocosecθ + cotθor ...

### 2 Symbol Order for Built-in Functions such as TrigReduce

1 answers, 87 views symbolic trigonometry order
I’d like to use the TrigReduce function on a sum of n sinusoids to any power, and am running into an issue with Mathematica’s default ordering of symbols. Is there a way that I can specify an order ...

### 2 Solve simple trig equation

5 answers, 3.980 views equation-solving trigonometry
I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to <...

### 1 Why is this function indeterminate?

1 answers, 57 views error series-expansion trigonometry
Consider an impulse train1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1)For x=0 it's clear that this function ...

### How can I avoid the message Infinity::indet?

2 answers, 85 views error series-expansion trigonometry
I have an impulse train of frequency R:1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1)For ...

### Force a result from “Indeterminate” for single impulse?

The formula for a single impulse of amplitude $1$ at $x=r$ is given by $$\frac {\sin (\pi (x-r))}{\pi (x-r)}$$ (In MathJax because it's a math formula.) Formally, at $x=r$, this function evaluates ...

### 1 Trigonometric simplification with assumptions fails

Consider the following inputAssuming[Element[y, Integers], (-1 + E^(I \[Pi] (x + y)))/(-1 + E^(I \[Pi] (x - y)))//FullSimplify] ...

### 1 Finding the mathematical function is plotted by using the bodeplot command

I've the following code: ...

### 2 Simplification of a product of trigonometric functions

3 answers, 131 views simplifying-expressions trigonometry
I have this expression2 Csc[2 y[x2]] Sech[x[x2]]^2 (Cos[y[x2]]^4 Cosh[x[x2]]^8 Sin[y[x2]]^4)^(1/4)which is 1. But Mathematica doesn't do the simplification. I ...

### Get the square root of a+bi,when a>0,b>0 in radical form

My code returns this result involves trigonometric functions, ...

### Plotting a function while varying a variable (on the x-axis) using two formulas [duplicate]

I want to plot the following function, where Rb is the variable (that has to be on the x-axis): ...

### 1 Not getting expected simplification of trigonometric expressions

I have two trigonometric expressions. I would like to eliminate the fraction from my 2nd expression. ...

### 1 Solve trig equation

2 answers, 60 views equation-solving trigonometry homework
I have a simple trig equation:Clear[f, x] f[x_] = Cos[2*x] - 3 Sin[x] + 2 Solve[f[x] == 0, x]I received a very long a complicated reply that I do not ...

### Plotting a function that has variables out of an other piece of code

I've the following code: ...

...

### 1 Substitution in trigonometric expressions to remove secant and cosecant functions

1 answers, 72 views replacement trigonometry
I manipulate equations which are trigonometric equations in mechanics. In theses equations, the custom is to use only Cos, Sin and Tan functions and not the secant and cosecant functions. To prevent ...

### Trig function graphing exercise [closed]

2 answers, 66 views plotting trigonometry homework
I am trying to figure out how to do the following exercise in Mathematica Graph $y(t)= a \cos t + b \sin t - 0.5 \sin t$ on the interval $0 ≤ t ≤ 6\, π$

### Verify solution of system of first order ODE

I am given a solution $v_1$(t)=$-e^{t/2}cost$ for a system of first order ODE and I am asked to verify this solution can solves the linear second order ODE in terms of $y_1$(t) Here is the matrix ...

### Solving a trig equation in a specific range

I want to define a function as suchg[n_] := Assuming[1<=x<=2, NSolve[n==-2 Cos[Pi x], x]]However the result comes out as a conditional expression, for ...

### How to get a single evaluation of RandomReal in a Block

I want to generate (and eventually sample) a sine wave with a random frequency in the range [½, 1] (i.e. capture somewhere between half and one period of the waveform over the domain [0,1]). The two ...

### User defined ArcTan function

I am trying to integrate an equation that requires an angle term calculated using ArcTan[x,y]. A number of issues have been mentioned about ...

### 4 How to solve this trigonometric system of equations numerically?

1 answers, 339 views equation-solving numerics trigonometry
How can the following trigonometric system of equations be solved numerically? ...

### 1 “Power series” in Cos[n*x] for X coordinate of planetary ellipse

1 answers, 123 views fitting trigonometry
Consider the functions below: ...

### 1 I want to graph all of ArcSin without restriction, how would I format that? [closed]

2 answers, 117 views plotting trigonometry
I am new to this and I've plotted this:Plot[3 ArcSin[x + 4] - 16, but I don't know what/how to specify the range?

### 37 How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I triedSolve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]It returns the ...

### 2 Axes labels as multiples of $\pi$

3 answers, 2.306 views plotting labeling trigonometry
I have a list as containing seven elements: ...

### 1 Determining the angle x through the point of intersection between lines in any triangle [closed]

I'm trying to determine the angle x in the triangle shown below. Given $\overline{DB}=\overline{DE}$ Given $\overline{AD}=\overline{DC}$ Given $\angle ADE=40^°$ Find $\angle DCB$ But I'm finding ...

### 7 Quantity and Trig functions

1 answers, 275 views trigonometry version-9 units
I have a bunch of data to which I've assigned units using Quantity, including some angular measurements in degrees. I'd like to be able to use these measurements ...

### 2 To solve this problem just follow this rule or is there another possibility?

5 answers, 149 views equation-solving trigonometry
To solve this problem just follow this rule or is there another possibility?Solve[(3 Sqrt[2])/Sin[60 Degree] == x/Sin[45 Degree], {x}]

### 5 Feature of quaternion Cos, Cot etc

0 answers, 125 views trigonometry quaternions
I am new to SE Mathematica, and search gives no answer; so here is my problem: During the testing of my numerical library for quaternions with Mathematica (package Quaternions) I observed the ...

### 1 Different solutions for $\sin (2x)-\cos (2x)= 1$ and $\sin(2x) = 1 + \cos(2x)$ [closed]

I am trying to solve an equation in Wolfram Mathematica and I get different results although the equation is technically the same. I am really confused. so basically: $\sin(2x) - \cos(2x)= 1$ is the ...

### 1 Equivalence of ComplexExpand and assuming real arguments

I am wondering why this simplification does not work,FullSimplify[Im[1/Sin[a]], Assumptions -> Element[a, Reals]] (*Out[1]= Im(csc(a))*)while this does:<...

### 1 Differential equation, Inverse Functions being used and a way to bypass it.

0 answers, 52 views differential-equations trigonometry
I have the following differential equation ...

### 1 How can Mathematica simplify this trigonometric function?

2 answers, 126 views simplifying-expressions trigonometry
This question must be too simple, but it confused me for several days. I want to know how can I do the following simplification using Mathematica: For example, convert ...

### 2 Error of InverseFunction

Update This bug has been fixed in v11.3.0. And as @Carl Woll has pointed out, the imaginary part of Sin and negative sign of Cos...

### 25 Extract real part of a complex expression better than Re does

1 answers, 22.269 views symbolic trigonometry
I have a complex expression with real positive variables only. Mathematica Input Style: ...

### 4 ArcTan apply to nested list

5 answers, 271 views list-manipulation trigonometry
I have a coordinate system generated by :coord = Table[{x, y}, {x, 5}, {y, 5}]I would like to calculate ArcTan(y/x) and ...

### 3 How to find non-overlapping triangles?

There are at least a few non-overlapping triangles made by the lines in the following graphic, how would I isolate them? ...

### Solve Parametric Equation

1 answers, 56 views equation-solving syntax trigonometry
This seems really easy and I'm probably just messing up on the syntax somewhere (I'm pretty new to Mathematica and I did pour through the Solve page trying to find an answer). I'm basically ...

### Cosine interpolation

1 answers, 299 views interpolation trigonometry
Suppose I have a list of values of a function $f(x)$ at positive integer points, say $$f(1) = -0.5, f(2) = -0.5, f(3) = 1, f(4) = -0.5, f(5) = -0.5, f(4) = 1,...$$ Can I interpolate a cosine function, ...